In typesetting by hand compositing, a sort or type is a piece of type representing a particular letter or symbol, cast from a matrix mould and assembled with other sorts bearing additional letters into lines of type to make up a form from which a page is printed.

From the invention of movable type up to the invention of hot metal typesetting essentially all printed text was created by selecting sorts from a type case and assembling them line by line into a form used to print a page. When the form was no longer needed all of the type had to be sorted back into the correct slots in the type case in a very time-consuming process called "distributing". This sorting process lead to the individual pieces being called sorts. It is often claimed to be the root of expressions such as "out of sorts" and "wrong sort", although this connection is disputed.

During the hot metal typesetting era, printing equipment used matrices to cast type as needed during the typesetting process. The popular Linotype cast entire lines of text at once rather than individual sorts, while the less popular competitor Monotype still cast the sorts individually. Later, when phototypesetting replaced hot metal typesetting, sorts disappeared entirely from the mainstream printing process.

Sort may refer to:

See also

A sorting algorithm is an algorithm that puts elements of a list in a certain order. The most-used orders are numerical order and lexicographical order. Efficient sorting is important for optimizing the use of other algorithms (such as search and merge algorithms) which require input data to be in sorted lists; it is also often useful for canonicalizing data and for producing human-readable output. More formally, the output must satisfy two conditions:

Further, the data is often taken to be in an array, which allows random access, rather than a list, which only allows sequential access, though often algorithms can be applied with suitable modification to either type of data.

Since the dawn of computing, the sorting problem has attracted a great deal of research, perhaps due to the complexity of solving it efficiently despite its simple, familiar statement. For example, bubble sort was analyzed as early as 1956. Comparison sorting algorithms have a fundamental requirement of O(n log n) comparisons (some input sequences will require a multiple of n log(n) comparisons); algorithms not based on comparisons, such as counting sort, can have better performance. Although many consider sorting a solved problem – asymptotically optimal algorithms have been known since the mid-20th century – useful new algorithms are still being invented, with the now widely used Timsort dating to 2002, and the library sort being first published in 2006.

In universal algebra and in model theory, a structure consists of a set along with a collection of finitary operations, and relations that are defined on it.

Universal algebra studies structures that generalize the algebraic structures such as groups, rings, fields and vector spaces. The term universal algebra is used for structures with no relation symbols.

Model theory has a different scope that encompasses more arbitrary theories, including foundational structures such as models of set theory. From the model-theoretic point of view, structures are the objects used to define the semantics of first-order logic. For a given theory in model theory, a structure is called a model, if it satisfies the defining axioms of that theory, although it is sometimes disambiguated as a semantic model when one discusses the notion in the more general setting of mathematical models. Logicians sometimes refer to structures as interpretations.

In database theory, structures with no functions are studied as models for relational databases, in the form of relational models.